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2026年9月8日(現地時間)、OpenAIがミレニアム懸賞問題の一つであるナビエ・ストークス方程式の存在と滑らかさの問題に対する解法を公開しました。数学界では、この成果が本来の懸賞が問う「外力なし」のケースではない点や、第三者による査読が未完了である点等から、評価には慎重です。証明を生成したのは“GPT-6 Astraより大幅に高性能な”社内モデルということで、公開されているモデルより高性能な「社内モデル」が次の高性能な公開モデルを開発するパターンが生まれているようです。 生成AIに、この件について深堀調査を行わせましたので、ご参照ください。なお、生成AIによる調査・分析結果は、公開された情報だけに基づくものであり、必ずしも実情を示したものではなく、誤った情報を含む可能性があることにご留意のうえ、ご参照ください。 On the Navier–Stokes Millennium Prize Problem https://openai.com/index/navier-stokes-solution/ An “Internal Model” That Outperforms GPT-6 Astra On September 8, 2026 (local time), OpenAI published a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. The mathematical community has been cautious in its assessment, however, noting, among other things, that the result does not address the “unforced” case specified in the original prize problem and that independent peer review has not yet been completed. The proof was reportedly generated by an internal model described as “significantly more capable than GPT-6 Astra.” A pattern therefore appears to be emerging in which internal models that outperform publicly available models are used to develop the next generation of more capable models for public release. I asked generative AI to conduct an in-depth investigation into this topic, and invite you to review the findings. Please bear in mind that the AI-generated research and analysis are based solely on publicly available information, may not necessarily reflect the actual state of affairs, and could contain inaccuracies. Your browser does not support viewing this document. Click here to download the document. Your browser does not support viewing this document. Click here to download the document. Your browser does not support viewing this document. Click here to download the document. Your browser does not support viewing this document. Click here to download the document. Your browser does not support viewing this document. Click here to download the document. Your browser does not support viewing this document. Click here to download the document.
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著者萬秀憲 アーカイブ
April 2026
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